Modelling a biological invasion of public health pest species using a population dynamics system

Biological invasion and range expansion are important areas of research especially for public health pests like mosquitoes, which are vectors for dengue diseases. In this work, a mathematical model incorporating competition, Allee effects and abiotic environmental factors is employed to describe mosquitoes’ vital interaction dynamics. By using dynamical systems and bifurcation analysis techniques, the model is demonstrated to possess a backward bifurcation under certain conditions. We also uncover some bifurcational changes in dynamics such as alternative stable states phenomenon, which can shape the transmission dynamics of viral infections. Overall, our findings provide fundamental knowledge on the crucial determinants of vector species spreads and the underlying mechanisms that can determine the transmission of vector-borne diseases.